Determination of the electric and dielectric constants of quartz

Abstract

In order to design electronic devices utilising quartz, a material of paramount importance in the electronic industry, a reliable set of the material constants and their temperature coefficients is required. The previously available data sets suffer from inconsistencies and inaccuracies in experimental and/or theoretical approach. The objective and result of this research was to provide a universally consistent and accurate data set of the elastic and dielectric moduli of quartz. An automated pulse-echo phase detection system for the measurement of acoustic delay time in highly parallel, orientated, single-crystal specimens was designed and built. Data for ten propagation modes in standard grade synthetic quartz were used to determine the six independent elastic moduli and their temperature coefficients to an accuracy better than 0.02% over the temperature range -60°C to 120°C using a frequency range of 10 MHz to 220 MHz. Computer control allowed the accumulation of several orders of magnitude more data than was acquired in previous experiments. This large data base enabled reliable calculations to be made of the parameters of the indium cold-weld bond used to attach the transducers. Use of this bonding technique allowed delay line measurements to be made to above 120°C, whereas the use of organic bonding agents had limited previous measurements to ~30°C. Comprehensive diffraction and transducer/bond reflection delay models were used to correct the experimental delay time data. An interferometric length measuring system was designed and used to measure specimen length. Capacitance measurements were performed to allow calculation of the dielectric moduli of quartz to an accuracy of 0.2%. The first fully documented and error-corrected measurements of the temperature coefficients of the dielectric moduli over the range -60°C to 120°C were also performed. An accurate hydrostatic and volumetric determination was made of the density of quartz. A full data set of the fundamental constants of standard grade synthetic quartz was thus compiled. Finally, the experimentally derived values of effective elastic moduli were varied within the experimental error to fit to the extremely sensitive curves of frequency versus temperature for singly and doubly rotated quartz resonators. Results show that the data set produced by this research is more reliable than other previously available data sets. Measurements on five propagation modes in very high purity synthetic quartz indicate that there may be a significant difference between this and standard grade synthetic quartz.